Problem: The arithmetic sequence $(a_i)$ is defined by the formula: $a_1 = 10$ $a_i = a_{i-1} + 5$ What is $a_{12}$, the twelfth term in the sequence?
Explanation: From the given formula, we can see that the first term of the sequence is $10$ and the common difference is $5$ To find the twelfth term, we can rewrite the given recurrence as an explicit formula. The general form for an arithmetic sequence is $a_i = a_1 + d(i - 1)$ . In this case, we have $a_i = 10 + 5(i - 1)$ To find $a_{12}$ , we can simply substitute $i = 12$ into the our formula. Therefore, the twelfth term is equal to $a_{12} = 10 + 5 (12 - 1) = 65$.